1. Relations and Functions
Chapter 2.1
Relations and Functions

2. Relations
A RELATION is a set of pairs of input and output values. EX Jobs, pay per hour.
These inputs and outputs can be written as an ordered pair.

3. Graphing
Graph the relation: {(-2,4), (3,-2), (-1,0), (1,5)}

4. Domain
The DOMAIN of a relation is the set of all inputs, or x-coordinates of the ordered pairs. {(-2,4), (3,-2), (-1,0), (1,5)} The domain is: {-2, -1, 1, 3}

5. Range
The RANGE of a relation is the set of all outputs, or y-coordinates of the ordered pairs. {(-2,4), (3,-2), (-1,0), (1,5)} The range is: {-2, 0, 4, 5}

6. Practice: Name the domain and range of each relations.
{(4, 2), (-1, 2), (3, 5)}
Domain:
Range:
{(1, -4), (3, 6), (5, 4)}

7. Mapping Diagram
Another way to show a relation is to use a mapping diagram, which links elements of the domain with corresponding elements of the range.

8. Mapping Diagram Example
Make a mapping diagram for the relation {(-1, -2), (3, 6), (-5, -10), (3, 2)}

9. You Try! Mapping Diagram
Make a mapping diagram for the relation {(0, 2), (1, 3), (2, 4), (-1, 3)}

10. Function
A FUNCTION is a relation in which each element of the domain is paired with exactly one element in the range.

11. FUNCTION
Domain Range 3 5 6 7 3 5 6 7

12. NOT A FUNCTION
Domain Range 3 5 6 7 3 5 6 7

13. You Try!
Make a Mapping Diagram for each relation, then determine if it is a function.
{(3, 4), (-1, 2), (5, 2)}
{(4, 2), (1, -5), (4, 3)}
{(5, -2), (5, 2), (6, 4)}

14. More About Relations
Relations can also be represented as a line, or a curve, not just as a couple of points. For example: y = x2

15. Another way to test function
Another way to tell if a relation is a function or not is to graph it on a coordinate plane. IF it passes the VERTICAL-LINE TEST, then the relation IS a function

16. Vertical Line Test
The Vertical Line Test is drawing a Vertical Line across the graphed relationship. IF a line crosses the relations more than once, it is not a function. IF all lines only cross the relations only once, it is a function.

17. Vertical-Line Test

18. Vertical Line Test

19. Functions?

20. Function Notation
F(x) ; You read the function notation as “f of x” or a “function of x.”

21. Evaluating Functions and Given the functions: Evaluate: f (-4)
3. f (2) + g (2)